The term `Exceptional Points' (EPs) has been introduced by T. Kato over
half a century ago[1]}. In mathematics, EPs are branch point
singularities of the spectrum and eigenfunctions for non-Hermitian (NH)
matrices[2]}, [3]}. In physics, EPs are the points for NH
Hamiltonian at which two or more eigenvalues and their corresponding
eigenvectors coalesce together[4]}, [5]}. Since the publication of
paper by Bender and Boettcher[6]}, EPs become one of most
interesting feature of NH physics. As a particular example, for NH
Hamiltonians with parity-time(\(\mathcal {PT}\) )-symmetry[7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, the spontaneous \(\mathcal {PT}\) -symmetry breaking corresponds to a typical
EP, at which energies levels become degenerate and eigenvectors coalesce. In
experiments, the phenomena of EPs had been realized and simulated by different
approaches[24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}, [36]}, [37]}, [38]}, [39]}, [40]}, [41]}, [42]}, [43]}, [44]}, [45]}, [46]}, [47]}, [48]}, , [49]}, [50]}, [51]}, [52]}, [53]}.
